Question

Oranges can be packed in sets of 10 oranges in box type a or 25 oranges in box type

b. a carton comprising of 1000 oranges of type a and b is packed. how many different combinations are possible in the number of type a and type b boxes while organizing the oranges?

a. 21

b. 20

c. 19

d. 18

Answer 1

answer is 21..

we can write problem in form of eqtn..

25*b+10*a=1000
now we have to find all posiible value of (a,b)..
so,
for satisfying eqtn "b" must be even & the range of "b" will varry from
0 to 40 so the total number is.... 21
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Answer 2

Box A can contain 10 oranges and Box B can contain 25 oranges so the equation is XA + YB=1000, we know the values for A&B so Equation becomes 10X + 25B=1000 => 2X + 5B=200, so fro the equation it is clear that the basic two values of X,Y are (0,40) & (100,0). Clearly if X increases by 5 then Y should decrease by 2 in order to maintain the constant value i.e 1000 oranges. so the different combinations will be (50,20) (55,18) (60,16) (65,14) (70,12) (75,10) (80,8) (85,6) (90,4) (95,2) (100,0) (45,22) (40,24) (35,26) (30,28) (25,30) (20,32) (15,34) (10,36) (5,38) (0,40 ) so there are 21 different combination by which we can arrange the oranges in the carton.